In the prior art, auxiliary lines consist of assemblies of tubes entirely made of steel. The dimensions of the tubes are determined in such a way that the tubes withstand the bursting stresses due to the internal/external pressure difference, the collapsible loads due to the internal pressure applied at the ends of the tubes and the tensile stresses exerted during hydraulic tests. Documents FR-01/10,360 and FR-01/10,361 are aimed to make auxiliary lines with hooped tubes. Using hooped tubes notably affords the advantage of reducing the steel thickness and therefore the weight of the tubes that constitute the auxiliary lines. However, the drawback of hooped tubes is that they have a lower flexural stiffness than the equivalent all-steel tubes for the same working pressure. Now, the tubes are subjected to collapsible loads generated by the internal/external pressure difference which causes what is referred to as a << bottom effect >> exerted on the ends of the tubes. Consequently, for the same bursting strength, a hooped tube has a smaller buckling length than the equivalent all-steel tube. The buckling length is the length of a tube from which it is likely to buckle when it is subjected to given collapsible loads. Considering the pressures to which the auxiliary lines may be subjected (1034 bars, i.e. 15,000 psi in working pressure), the hooped tubes that constitute the auxiliary lines on a riser are likely to buckle. To avoid this problem, it is possible to link the hooped tube elements to the main tube by means of clamps. The clamps hold the hooped tube elements in relation to the main tube, but they allow the hooped tube elements to freely slide in relation to the main tube in the direction of the riser axis. However, the use of clamps can be incompatible with the use of floats on the riser. It is usual to arrange floats over the length of the riser to reduce the tension at the riser top. The floats must have a minimum length to minimize manufacturing costs. This minimum length requires a length between two clamps that is sometimes incompatible with the minimum buckling length at the working pressure.